Abstract
AbstractThe Gutenberg‐Richter b value is commonly used in volcanic eruption forecasting to infer material or mechanical properties from earthquake distributions. Such studies typically analyze discrete time windows or phases, but the choice of such windows is subjective and can introduce significant bias. Here we minimize this sample bias by iteratively sampling catalogs with randomly chosen windows and then stack the resulting probability density functions for the estimated value to determine a net probability density function. We examine data from the El Hierro seismic catalog during a period of unrest in 2011–2013 and demonstrate clear multimodal behavior. Individual modes are relatively stable in time, but the most probable value intermittently switches between modes, one of which is similar to that of tectonic seismicity. Multimodality is primarily associated with intermittent activation and cessation of activity in different parts of the volcanic system rather than with respect to any systematic inferred underlying process.
Highlights
IntroductionIn contrast the reported b values from published studies of earthquake populations associated with volcanic unrest are commonly reported as being significantly higher than this [Roberts et al, 2015]
The b value of the Gutenberg-Richter relation, log(N) = a À bM [Gutenberg and Richter, 1954], describes the relative proportions of large- and small-magnitude earthquakes in a catalog
The method minimizes bias associated with finite sampling of time windows and reveals a complex net probability density function in the real volcanic data
Summary
In contrast the reported b values from published studies of earthquake populations associated with volcanic unrest are commonly reported as being significantly higher than this [Roberts et al, 2015]. The errors in the b values are likely to be large, correlated, and underestimated, and potentially give rise to biased results [Roberts et al, 2015]. At this stage of modeling we do not consider the effect of uncertainties in the individual magnitudes, so our error estimates are all underestimates to some extent
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